To what extent can ethics and foreign policy be conceived as possible? Instead of answering within the implied dichotomy of possibility and impossibility, this thesis argues for a reconceptualisation of the dichotomy. Ethics and foreign policy are better understood on the basis of undecidability: neither simply possible nor impossible, but both at the same time. A deconstructive reading of British (1997-2006) and EU (1999- 2004) foreign policy, both of which make claims to ethics, reveals how the issue is beset by internal contradictions, paradoxes and aporias. The deconstruction is structured around the concepts of subjectivity, responsibility and hospitality, each of which constitutes an important point of undecidability within British and EU representations of their ethical dimension. The subject of ethics and foreign policy is always haunted and inhabited by its object, responsibility is necessarily irresponsible, and hospitality contains an irrepressible hostility. Thus, ethics and foreign policy is best conceived as undecidably im-possible. However, such undecidability cannot be used to justify abandoning the goal of an ethical foreign policy. Rather, a Derridean 'negotiation' is proposed. Negotiation seeks to remain loyal to the dual injunction of deconstruction, an undecidability which is the condition of ethics and politics, and a decision which decides, and closes to certain figures of otherness. It requires a permanent questioning, testing and invention of the promise of ethics and foreign policy. This produces a range of illustrative suggestions for the possible enactment of an ethico-political foreign policy, which would refer to and strive for an ultimately unrealisable ethical foreign policy. This research contributes a fundamental critique and questioning of the possibility of ethics and foreign policy. It provides a revealing exploration of British and EU foreign policy from the period, based around responsibility and hospitality. Finally, the thesis introduces the Derridean notion of negotiation to the discipline, seen as a way of moving through the potential paralysis brought by the undecidability arising from foundational questioning.